The Roper Organization conducted identical surveys in 1995...

The Roper Organization conducted identical surveys in 1995 and $2005 .$ One question asked women was "Are most men basically kind, gentle, and thoughtful?" The 1995 survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. In 2005,1,530 of the 3,000 women surveyed thought that men were kind, gentle, and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in 2005 compared with $1995 ?$

Key Concepts

Statistical Hypothesis Testing

This is the process used to evaluate whether a claim about a population parameter is supported by sample data. In particular, it involves stating a null hypothesis (usually a statement of no effect or equality) and an alternative hypothesis (which represents the claim being tested), then using data to decide if there is enough evidence to reject the null hypothesis.

Null and Alternative Hypotheses

These represent the two competing explanations in a hypothesis test. The null hypothesis typically asserts that there is no difference or effect between groups, while the alternative hypothesis suggests that there is a difference. In comparative studies, specifying these clearly and correctly is vital for determining the direction and nature of the test, such as whether it is one-tailed or two-tailed.

Two-Sample Proportion Test

This type of test is used to compare two proportions from independent samples to determine if there is a statistically significant difference between them. It involves calculating sample proportions, estimating the standard error for the difference between these proportions, and then computing a test statistic based on these estimates.

One-Tailed Test

A one-tailed test is used when the research interest lies in determining if one proportion is specifically less than or greater than another. This directionality affects how the rejection region is defined for the test statistic and is particularly important when a hypothesis predicts a decrease or increase rather than just any difference.

Significance Level and p-value

The significance level (commonly denoted as alpha, e.g., 0.05) is the threshold set by the researcher for deciding whether to reject the null hypothesis. The p-value is the probability of obtaining results as extreme as those observed, under the assumption that the null hypothesis is true. Comparing the p-value to the significance level helps determine if the observed effect is statistically significant.

Transcript

00:01 This organization performed two surveys in 1995 and in 2005 and asked women are men generally kind, gentle, etc.

00:12 And so we're going to assume that the proportion from the first survey is equal to the proportion of the second survey.

00:19 And alternately, that the proportion is actually less for that second survey and that it's gone down.

00:30 Basically.

00:31 So here we could say even less than or equal to them instead of the quality depending on the way your instructor is having you work.

00:37 So we're using a 5 % significance level and for this setting then we know we want to put all 5 % in the upper tail and that would correspond with a z value of 1 .645.

00:51 So this is where we would be rejecting this is where we would be rejecting the null if we have our test statistic up here.

00:58 So let's look at what our test statistic it's going to be we have our first proportion from the first group was 2010 out of 3 ,000 and our second proportion for the second survey was still out of 3 ,000 and that was 1 ,530 so oh boy that looks different doesn't it and our pooled value will be a total of 6 ,000 people were surveyed and then we need to add these to and that looks like 3 ,540 and we get these values.

01:35 This proportion is 0 .67.

01:38 This one is 0 .51, and this pooled value is 0 .59.

01:44 So nicely, they come out as nice decimals.

01:46 And so let's calculate our test statistic and do our comparison so we can make our decision...

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